By Soo T. Tan

Combining the easiest of conventional insurance with sleek instruments, market-leading *Applied Calculus for the Managerial, lifestyles, and Social Sciences: a quick Approach*, 8th variation, applies math in your international. It can provide simply the appropriate stability of purposes, pedagogy, and know-how that can assist you reach the path. educating by means of program, the textual content is jam-packed with real-life examples that encourage and enlighten you. Its intuitive method introduces summary thoughts via examples drawn from universal reviews to you can relate. it's also perception from pros approximately how they combine math into their day by day operations. a variety of workouts, together with Diagnostic checks, make sure you have an outstanding figuring out of textual content strategies sooner than advancing to the following topic—or examination. an exhilarating array of supplements—Enhanced WebAssign, answer video clips, own Tutor—equips you with large studying aid that is helping maximize your research efforts and enhance your grade. putting off the apprehension many scholars believe after they start this direction, *Applied Calculus for the Managerial, existence, and Social Sciences: a quick Approach*, 8th variation, makes use of an available presentation of innovations and techniques that makes it a good source for majors and non-majors alike.

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5, where y is the number of families with an income of x or more dollars. a. How many families in this city have an income of $30,000 or more? b. How many families have an income of $60,000 or more? 140. If b2 Ϫ 4ac Ͼ 0, then ax2 ϩ bx ϩ c ϭ 0 (a real roots. 0) has two 141. If b2 Ϫ 4ac Ͻ 0, then ax2 ϩ bx ϩ c ϭ 0 (a real roots. 0) has no 142. 21a ϩ b 2 1b Ϫ a2 ϭ 2b2 Ϫ a2 for all real numbers a and b. c. How many families have an income of $150,000 or more? 2 Precalculus Review II Rational Expressions Quotients of polynomials are called rational expressions.

2y Bx 3 2x2y 74. 2x 103. 2xϪ5/2 Ϫ 104. 2 3 Ϫ3/2 x 2 1 2 3/2 ¢ u Ϫ 2u1/2≤ 2 3 In Exercises 105–118, factor each expression completely. In Exercises 75–96, perform the indicated operations and simplify each expression. 105. 6ac ϩ 3bc Ϫ 4ad Ϫ 2bd 75. (7x2 Ϫ 2x ϩ 5) ϩ (2x2 ϩ 5x Ϫ 4) 106. 3x3 Ϫ x2 ϩ 3x Ϫ 1 76. (3x2 ϩ 5xy ϩ 2y) ϩ (4 Ϫ 3xy Ϫ 2x2) 107. 4a2 Ϫ b2 108. 12x2 Ϫ 3y2 77. (5y2 Ϫ 2y ϩ 1) Ϫ (y2 Ϫ 3y Ϫ 7) 109. 10 Ϫ 14x Ϫ 12x2 110. x2 Ϫ 2x Ϫ 15 111. 3x2 Ϫ 6x Ϫ 24 112. 3x2 Ϫ 4x Ϫ 4 113. 12x2 Ϫ 2x Ϫ 30 114.

5 Ͻ Ϫ3, so Ϫ5 ϩ 2 Ͻ Ϫ3 ϩ 2; that is, Ϫ3 Ͻ Ϫ1. Ϫ5 Ͻ Ϫ3, and since 2 Ͼ 0, we have (Ϫ5)(2) Ͻ (Ϫ3)(2); that is, Ϫ10 Ͻ Ϫ6. Ϫ2 Ͻ 4, and since Ϫ3 Ͻ 0, we have (Ϫ2)(Ϫ3) Ͼ (4)(Ϫ3); that is, 6 Ͼ Ϫ12. Similar properties hold if each inequality sign, Ͻ, between a and b and between b and c is replaced by Ն, Ͼ, or Յ. Note that Property 4 says that an inequality sign is reversed if the inequality is multiplied by a negative number. A real number is a solution of an inequality involving a variable if a true statement is obtained when the variable is replaced by that number.